arXiv subjects
Publications and source records attributed to Béchir Amri.
We present an integral product formula for Jack polynomials of two variables, extending that of zonal polynomials. It provides another way to find the explicit integral representation for the generalized Bessel function of type $ B_2 $, as presented in \cite{D}.
The present paper studies structure of the ring of integer-valued entire functions. We characterize certain classes of prime and maximal ideals and investigate some of their properties.
In this paper, we introduce a discrete Riesz transforms associated with the non-symmetric trigonometric Heckman-Opdam polynomials of type $A_1$. We prove that they can be extended to a bounded operators on $\ell^p(\mathbb{Z})$, $1<p<\infty$.
Let $L_k=-Δ_k+V$ be the Dunk- Schrödinger operators, where $Δ_k=\sum_{j=1}^dT_j^2$ is the Dunkl Laplace operator associated to the dunkl operators $T_j$ on $\mathbb{R}^d$ and $V$ is a nonnegative potential function. In the first part of this paper we introduce the Riesz transform $R_j= T_j L_k^{-1/2}$ as an $L^2$- bounded operator and we prove that is of weak type $(1,1)$ and then is bounded on $L^p(\mathbb{R}^d,dμ_k(x))$ for $1<p\leq 2$. The second pat is devoted to the $L^p$ smoothing of the semigroup generated by $L_k$, when $V$ belongs to the standard Koto class.
In this paper, we are interested in the estimates of the Dunkl Kernel on some special sets, following the work of M.F.E. de Jeu and M. Rösler in \cite{R3}.
In this paper, our main aim is to derive $L^p-L^q$ estimates of the solution $u_k(x,t)$ ( t fixed) of the Cauchy problem for the homogeneous linear wave equation associated to the Dunkl Laplacian $Δ_k$, $$Δ_ku_k(x,t)= \partial_t^2u_k (x,t),\quad \partial_tu_k(x,0)= f(x),\quad u_k(x,0)= g(x).$$ We extend to Dunkl setting the estimates given by Srichartz in \cite{Sti} for the ordinary wave equation .
The aim of this paper is to give an explicit formula for the nonsymmetric Heckman-Opdam's hypergeometric function of type $A_2$. This is obtained by differentiating the corresponding symmetric hypergeometric function.
In this paper, we study the $L^p$ boundedness of a class of oscillating multiplier operator for the Dunkl transform, $T_{m_α}=\mathcal{F}_k^{-1}(m_α\mathcal{F}_k(f))$ with $m(ξ)=|ξ|^{-α}e^{\pm i|ξ|}ϕ(ξ)$. We obtain an $L^p$-bound result for the corresponding maximal functions. As a specific applications, we give an extension of the $L^p$ estimate for the wave equation and of Stein's theorem for the analytic family of maximal spherical means \cite{Stein}
We give an explicit integral formula for the Dunkl kernel associated to root system of type $A_2$ and parameter $k>0$, by exploiting recent result in [1].
Through the theory of Jack polynomials we give an iterative method for integral formula of Dunkl-Bessel functions of type $A_{N-1}$ and a partial product formula for it.
In the present paper, we establish that Riesz transforms for Dunkl Hermite expansion as introduced in [4] are singular integral operators with Hörmander's type conditions and we show that are bounded on $L^p(\mathbb{R}^d; dμ_k) 1 < p < 1.
In this paper we obtain the $L^p$-boundedness of Riesz transforms for Dunkl transform for all $1<p<\infty$.
In this article, we establish first a geometric Paley-Wiener theorem for the Dunkl transform in the crystallographic case. Next we obtain an optimal bound for the $L^p\to L^p$ norm of Dunkl translations in dimension 1. Finally we describe more precisely the support of the distribution associated to Dunkl translations in higher dimension.